Post on 08-Apr-2018
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FINANCE
12. Capital Structure and Cost of Capital
Professor Andr Farber
Solvay Business School
Universit Libre de Bruxelles
Fall 2004
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Risk and return and capital budgeting
Objectives for this session:
Beta of a portfolio
Beta and leverage
Weighted average cost of capital
Modigliani Miller 1958
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Beta of a portfolio
Consider the following portfolio
Stock Value Beta
A nA v PA FA
B nB v PB FB
The value of the portfolio is:V= nA v PA
+ nA v PB
The fractions invested in each stock are:
Xi
= ( niP
i) / V fori = A,B
The beta of the portfolio is the weighted average of the betas of the
individual stocks
FP= XA FA + XB FB
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Example
Stock $ F X
ATT 3,000 0.76 0.60
Genetech 2,000 1.40 0.40
V 5,000
FP = 0.60 * 0.76 + 0.40 * 1.40 = 1.02
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Application 1: cost of capital for a division
Firm = collection of assets
Example: A company has two divisions
Value($ mio) F
Electrical 100 0.50
Chemical 500 0.90 V 600
Ffirm = (100/600) * (0.50) + (500/600) * 0.90 = 0.83
Assume: rf= 5% rM - rf = 6%
Expected return on stocks: r= 5% + 6% v 0.83 = 9.98 %
An adequate hurdle rate for capital budgeting decisions ? No
The firm should use required rate of returns based on project risks:
Electricity : 5 + 6 v 0.50 = 8% Chemical : 5 + 6 v 0.90 = 10.4%
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Application 2: leverage and beta
Consider an investor who borrows at the risk free rate to invest in the
market portfolio
Assets $ F X
Market portfolio 2,000 1 2
Risk-free rate -1,000 0 -1 V 1,000
FP = 2 v 1 + (-1) v 0 = 2
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8%
14%
1 2 Beta
M
P
8%
14%
20%
Sigma
Expected ReturnExpected Return
M
P
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Cost of capital with debt
Up to now, the analysis has proceeded based on the assumption that
investment decisions are independent of financing decisions.
Does
the value of a company change
the cost of capital change if leverage changes ?
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An example
CAPM holds Risk-free rate = 5%, Market risk premium = 6%
Consider an all-equity firm:
Market value V 100
Beta 1
Cost of capital 11% (=5% + 6% * 1) Now consider borrowing 10 to buy back shares.
Why such a move?
Debt is cheaper than equity
Replacing equity with debt should reduce the average cost of
financing
What will be the final impact
On the value of the company? (Equity + Debt)?
On the weighted average cost of capital (WACC)?
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Weighted Average Cost of Capital
An average of:
The cost of equity requity
The cost of debt rdebt
Weighted by their relative market values (E/Vand D/V)
Note: V= E+ D
V
Dr
V
Err debtequitywacc vv|
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ModiglianiMiller (1958)
Assume perfect capital markets: not taxes, no transaction costs
Proposition I:
The market value of any firm is independent of its capital structure:
V= E+D = VU
Proposition II:
The weighted average cost of capital is independent of its capital
structure
rwacc = rA
rA isthecostofcapitalofan allequityfirm
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UsingMM 58
Value of company: V= 100
Initial Final
Equity 100 80
Debt 0 20
Total 100 100 MM I
WACC = rA 11% 11% MM II
Cost of debt - 5% (assuming risk-free debt)
D/V 0 0.20
Cost of equity 11% 12.50% (to obtain rwacc = 11%)
E/V 100% 80%
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Why is rwacc unchanged?
Consider someone owning a portfolio of all firms securities (debt and
equity) with Xequity = E/V (80% in example ) and Xdebt= D/V (20%)
Expected return on portfolio = requity * Xequity +rdebt * Xdebt
This is equal to the WACC (see definition):rportoflio = rwacc
But she/he would, in fact, own a fraction of the company. The expected
return would be equal to the expected return of the unlevered (all equity)
firm
rportoflio = rA The weighted average cost of capital is thus equal to the cost of capital of
an all equity firm
rwacc = rA
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What are MM I and MM II related?
Assumption: perpetuities (to simplify the presentation)
For a levered companies, earnings before interest and taxes will be split
between interest payments and dividends payments
EBIT = Int+ Div
Market value of equity: present value of future dividends discounted at thecost of equity
E= Div / requity
Market value of debt: present value of future interest discounted at the cost
of debt
D = Int/ rdebt
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Relationship between the value of company and
WACC
From the definition of the WACC:
rwacc * V= requity * E+rdebt * D
As requity * E= Div and rdebt * D = Int
rwacc * V= EBIT
V= EBIT/rwacc
Market value of
levered firm
EBIT is
independent of
leverage
If value of company
varies with leverage, so
does WACC in
opposite direction
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MM II: another presentation
The equality rwacc = rA can be written as:
Expected return on equity is an increasing function of leverage:
E
Drrrr debtAAequity v! )(
rA
D/E
requity
11%
rdebt
5%
0.25
12.5%
rwacc
Additionalcostduetoleverage
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Why does requity increases with leverage?
Because leverage increases the risk of equity.
To see this, back to the portfolio with both debt and equity.
Beta of portfolio: Fportfolio = Fequity * Xequity +Fdebt * Xdebt
But also: Fportfolio = FAsset So:
or
DE
D
DE
E
DebtEquityAsset
v
v!
E
D
DebtAssetAssetEquity v! )( FFFF
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Back to example
Assume debt is riskless:
E
V
E
DAssetAssetEquity FFF !! )1(